On the Statistical Invariance for Adaptive Radar Detection in Partially Homogeneous Disturbance Plus Structured Interference

This paper deals with the problem of adaptive vector subspace signal detection in partially homogeneous Gaussian disturbance and structured (unknown) deterministic interference within the framework of invariance theory. It is first proved that the Maximal Invariant Statistic (MIS) for the problem at hand is scalar-valued and coincides with the well-known adaptive normalized matched filter evaluated after data projection in the complementary subspace of the interfering signal. Second, the statistical characterization of the MIS under both hypotheses is derived. Then, it is shown the statistical equivalence of (two-step) generalized-likelihood ratio test, Rao and Wald tests, as well as the more recently considered Durbin and Gradient test, to the above statistic. Finally, simulation results are provided to confirm our findings and analyze the performance trend of the MIS with the relevant parameters.